Non-elliptical contact profile for roller bearing

ABSTRACT

A roller bearing includes an inner race ring, an outer race ring, and a roller arranged between and in contact with the inner and outer rings. The bearing has a flange (31,131) on the inner race ring at one axial end, and a flange (21,121) on the outer race ring at an opposite axial end. One of the flanges, and/or an end of the roller, includes at least one principal segment (53,153) intermediate two additional segments (52,152; 54,154). The principle segment is tangentially blended with the two additional segments, and the principle segment has a first curvature that is different from the respective curvatures of the two additional segments. A non-elliptical contact footprint can be obtained by composite profiles at the contact location between the roller end and the mating flange face.

RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication No. 62/490,392 filed Apr. 26, 2017, and U.S. ProvisionalPatent Application No. 62/519,464 filed Jun. 14, 2017, the content ofboth applications is hereby incorporated by reference herein.

BACKGROUND

The present invention relates to bearings, and more particularly toroller bearings.

Radial cylindrical bearings are used primarily to bear a substantialamount of radial load. Modern applications however require such bearingsto also bear a certain amount of axial load. In these cases, the rollerend and the mating faces on the inner and outer flanges of the bearingrings have to be properly designed to produce adequate contactfootprints to manage contact stress and friction. Prior art designs,such as those disclosed in U.S. Pat. No. 6,530,693 B1 and U.S. Pat. No.6,997,616 B2, propose profiled roller ends that result inelliptical-shaped contact portions or footprints between roller ends andflange faces. The shapes of the contact ellipses are determined by theprincipal radii at the center of the contact, and are independent ofcontact load. The size of the contact ellipse increases as the contactload increases. To prevent the contact footprint from having undesiredinteraction (e.g., truncation) with the edges of the flange face createdby the undercut and outer diameter or inner diameter surface geometry,which leads to severe edge stresses, the contact ellipses are designedwith their semi-major axis lying in the circumferential direction. Atlight loads, however, when the periphery of the contact ellipse is faraway from the edges of the flange face, the shape of the contactfootprint ellipse may not be the most desirable for managing the contactstress.

SUMMARY

A first aspect of the invention provides a profile at the roller endand/or the mating flange face that produces a non-elliptical footprintat the contact between the roller end and the mating flange faces. Inanother aspect, the invention provides a profile on the roller end faceand/or flange face that contains multiple radii of curvature. Yetanother aspect of the current invention is to produce a profile thatcontains a multi-segmented profile portion on the roller end and/orflange face with each profile segment being tangent to at least one ofthe adjacent profile segments. Another aspect of the current inventionis to produce a profile on the roller end face and/or the flange facethat contains a segment of a logarithmic profile in the contact portion.

More specifically, in one embodiment, the invention provides a rollerbearing including an inner race ring, an outer race ring, and a rollerarranged between and in contact with the inner and outer rings. Thebearing has a flange on the inner race ring at one axial end, and aflange on the outer race ring at an opposite axial end. The roller has aprofiled roller end including at least one principal segmentintermediate two additional segments. The principle segment istangentially blended with the two additional segments, and the principlesegment has a first curvature that is different from the respectivecurvatures of the two additional segments.

In another embodiment, the invention provides a roller bearing includingan inner race ring, an outer race ring, and a roller arranged betweenand in contact with the inner and outer rings. The bearing has a flangeon the inner race ring at one axial end, and a flange on the outer racering at an opposite axial end. At least one of the flanges is profiledto include at least one principal segment intermediate two additionalsegments. The principle segment is tangentially blended with the twoadditional segments, and the principle segment has a first curvaturethat is different from the respective curvatures of the two additionalsegments.

In yet another embodiment, the invention provides a roller bearingincluding an inner race ring, an outer race ring, and a roller arrangedbetween and in contact with the inner and outer rings. The bearing has aflange on the inner race ring at one axial end, and a flange on theouter race ring at an opposite axial end. At least one of the flanges,or an end of the roller, has a profile including a principal segmentwith a reference point C defining a contact location between the rollerand the flange, the principal segment having a continuously changingradius of curvature that decreases as a distance from the referencepoint C increases. In many embodiments, the reference point C may be atthe center of the principal segment, but this need not be the case.

Other aspects of the invention will become apparent by consideration ofthe detailed description and accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a perspective view, partially cut-away, of a rolling elementbearing embodying the present invention.

FIG. 2 is a perspective view of a rolling element of the rolling elementbearing of FIG. 1.

FIG. 3 is a schematic view of the rolling element of FIG. 2,illustrating a portion of the curved end face profile.

FIG. 4 schematically illustrates the contact footprint between therolling element of FIG. 3 and the mating flange face of the rollingelement bearing.

FIG. 5 schematically depicts an alternative embodiment of the inventionin which the roller end profile is spherical and the mating flange facehas at least three profile segments.

FIG. 6 schematically depicts another alternative embodiment of theinvention in which the roller end profile is conical and the matingflange face has at least three profile segments.

FIG. 7 is a perspective view, partially cut-away, of another rollingelement bearing embodying the present invention.

FIG. 8 is a perspective view of a rolling element of the rolling elementbearing of FIG. 7.

FIG. 9 is a schematic view of the rolling element of FIG. 8,illustrating a portion of the curved end face profile.

FIG. 10 is an enlarged partial view of the schematic view of FIG. 9.

FIG. 11 is a graphical view showing the curvature of a portion of thecurved end face profile of FIG. 9.

FIG. 12 schematically illustrates the contact footprint between therolling element of FIG. 9 and the mating flange face of the rollingelement bearing.

FIG. 13 schematically depicts another alternative embodiment of theinvention in which the roller end profile is conical and the matingflange face has at least three profile segments, with at least onesegment being a portion of a logarithmic curve.

DETAILED DESCRIPTION

Before any embodiments of the invention are explained in detail, it isto be understood that the invention is not limited in its application tothe details of construction and the arrangement of components set forthin the following description or illustrated in the following drawings.The invention is capable of other embodiments and of being practiced orof being carried out in various ways.

Referring to FIG. 1, a roller bearing or rolling element bearing 10 ofthe current invention includes an outer ring 20, an inner ring 30, and aset of rollers 40 arranged between and in rolling contact with the outerand inner rings 20 and 30. While the illustrated embodiment shows acylindrical roller bearing (with cylindrical rollers), the invention canalso be applied to tapered roller bearings, spherical roller bearings,and possibly, needle roller bearings. The outer ring 20 includes atleast one radially inwardly-extending flange 21 at one end of theraceway 22 defined on the outer ring 20. In the illustrated embodiment,the outer ring 20 includes two radially inwardly-extending flanges 21.Each flange 21 includes a flange face 23 facing axially inwardly towardthe raceway 22.

The inner ring 30 includes at least one radially outwardly-extendingflange 31 at one axial end of the raceway 32 defined on the inner ring30. The flange 31 includes a flange face 33 facing axially inwardlytoward the raceway 32.

Each roller 40 has two end faces 41 a and 41 b, and an outer diametersurface 46 that engages and rolls on the raceways 22, 32. The end faces41 a, 41 b may be made substantially symmetrical to a center radialplane (a plane perpendicular to roller axis) of the roller 40, howeverthis need not be the case.

With reference to FIGS. 2 and 3, each end face 41 a, 41 b contains acurved profile 45 defined in an axial plane through a rotational axis 47(see FIG. 3) of the roller 40. The curved profile 45 is formed bymultiple segments 51, 52, 53, 54, and 55 as, for example, shown in FIGS.2 and 3. It is to be understood that in FIG. 3, only the lower rightcorner of the roller 40 is illustrated with the profile 45 forsimplicity and clarity, but that at least the upper right corner of theend face 41 b would have the same profile mirrored about the axis 47.Likewise, the end face 41 a could include the same profile 45 mirroredabout the axial center-point of the roller 40. Each profile segment 51,52, 53, 54 and 55 is defined by a mathematically defined curvature. Theprofile segment 51 is a portion of a straight line whose curvatureradius is infinity. Profile segments 52 to 55 are portions of circleswith curvature radii of R_(A2), R_(B2), R_(C2), and R_(D2),respectively. The centers of these curvatures are at O_(A2), O_(B2),O_(C2), and O_(D2), respectively. Profile segments 51 and 52 are blendedat a tangent point A. Profile segments 52 and 53 are blended at atangent point B. Profile segments 53 and 54 are blended at a tangentpoint C. Profile segments 54 and 55 are blended at a tangent point D.Profile segment 55 is blended with the outer diameter surface 46 of theroller 40 at point E. Unlike the other blending points (A-D), point Emay or may not be a tangent point. The profile segment 55 is optional.In cases where the profile segment 55 is not used, profile segment 54can be blended directly with outer diameter surface 46 at a non-tangentpoint.

The locations of the profile segments 51, 52, 53, 54 and 55 of therollers 40 are designed such that when the roller 40 is assembled andset in operation in a bearing 10 under thrust load, the contact betweenthe roller end 41 a or 41 b and the mating flange face 23 and/or 33starts at point 61 (see FIGS. 4-6). Referring to FIG. 4, a contact patchor footprint 62 is developed as contact load increases. The contactfootprint 62 remains elliptical or circular in shape when the contactload is relatively low before reaching a load threshold of Q_(min). Thisellipse or circle corresponds to profile segment 53 (BC) with thecurvature radius R_(B2). As the load continues to increase, the contactfootprint 62 starts to deviate from its original elliptical or circularshape. Specifically, the contact footprint 62 is truncated by segment 52(AB) at the upper side and by segment 54 (CD) at the lower side, andassumes a non-ellipse or non-elliptical shape as represented in the areabetween 65 and 62. As the load further increases, the aspect ratio(length over width) of the contact footprint 62 increases, and reaches apredetermined or desirable value for optimal contact attributes, such asflange torque and/or wear rate, under a predetermined design loadQ_(max). At load Q_(max), the contact footprint is represented by 65,and is non-elliptical in shape.

To achieve the above mentioned non-elliptical shape during contact, thecurvature center O_(B2) of the profile segment 53 may be offset from orlocated at a distance from the roller axis 47 that is within (smallerthan) a distance DS₁ (see FIG. 3). Likewise, the centers of curvaturesfor other profile segments may be offset from or located at distancesfrom the roller axis 47 that is outside or above (greater than) DS₂ (seeFIG. 3). DS₁<0.5R, and DS₂>0.5R, where R is the radius of roller body.

It should be noted that to achieve the above-mentioned non-ellipticalcontact footprint, profile segments 52 and 54 adjacent to the principalprofile segment 53 need not be portions of circles. They can be, forexample, a portion of exponential curves and/or logarithm curves. In yetother embodiments (such as discussed below with respect to FIGS. 7-13),the principle profile segment 53 could be a portion of exponentialcurves and/or logarithm curves.

The above-mentioned multi-radius profile or multi-segment profile onroller end faces can also, or alternatively, be made on flange faces 23and/or 33. FIGS. 5 and 6 illustrate the flange faces 33, but can alsorepresent the flange faces 23.

FIG. 5 depicts a portion of a roller bearing having rollers 40′ withspherical roller ends 41′. The profile of the roller end 41′ isdescribed by a single radius curve (R_(B2)) with the center of curvatureat the rotation axis 47 of the roller. The roller 40′ is brought intocontact with inner ring 30′ of the bearing during operation. The contactoccurs at the mating flange face 33′ having at least three profilesegments 34, 35, and 36. Each profile segment 34, 35, and 36 may bemathematically described by a radius of curvature. The radius ofcurvature (R_(B1)) for the second profile segment 35 can be infinity,that is to say the second profile segment is a straight line. The firstprofile segment 34 is designed to be tangent to the second profilesegment 35. The second profile segment 35, in turn, is tangent to thethird profile segment 36. The first profile segment 34 is blended to theouter diameter 37 of the flange 31′ at a non-tangent point. The thirdprofile segment 36 is blended to the undercut 38 of the flange atanother non-tangent point. When the roller 40′ is brought into contactwith the mating flange 31′ at the contact point 61′, anelliptically-shaped or circular contact footprint initially develops.The elliptically-shaped or circular contact footprint corresponds to thecurvature radius R_(B2) of the roller end 41′. As the load is increased,the ellipse is truncated by profile segment 34″ at the upper side and byprofile segment 36″ at the lower side. The aspect ratio of the truncatedellipse increases as the contact load increases.

FIG. 6 depicts a roller bearing having rollers 40″ that have conicalroller ends 41″. The profile of the mating face 33″ of the flange 31″ ismathematically described by multi-radius curves. The profile has atleast three segments 34″, 35″, and 36″. Any two adjacent segments aretangent to each other. When the roller 40″ is brought into contact withthe mating flange 31″ at the contact point 61″, an elliptically-shapedor circular contact footprint initially develops. Theelliptically-shaped or circular contact footprint corresponds to thecurvature radius R_(B1) of the profile segment 35″. As the load isincreased, the ellipse is truncated by profile segment 34″ at the upperside and by profile segment 36″ at the lower side. The aspect ratio ofthe truncated ellipse increases as the contact load increases. At apredetermined design load for the bearing, the contract footprint isnon-elliptical.

A non-elliptical contact footprint can be obtained by composite profilesat the contact location between the roller end and the mating flangeface. This is to say that multi-radius profiles or multi-segmentprofiles can be placed either on the roller end, on the flange face, oron both the roller end and the flange faces. The profile segment (orsegments) at the center of the contact footprint has a radius ofcurvature that is substantially greater than that of the segmentsadjacent to that center segment. At a predetermined design load for thebearing, the contract footprint is non-elliptical.

FIGS. 7-11 illustrate another embodiment of a roller or rolling elementbearing 100 of the current invention. Referring to FIG. 7, the bearing100 includes an outer ring 120, an inner ring 130, a set of rollers 140arranged between and in rolling contact with the outer and inner rings120, and 130. While the illustrated embodiment shows a cylindricalroller bearing (with cylindrical rollers), the invention can also beapplied to tapered roller bearings, spherical roller bearings, and,possibly, needle roller bearings. The outer ring 120 includes at leastone radially inwardly-extending flange 121 at one end of the raceway 122defined on the outer ring 120. In the illustrated embodiment, the outerring 120 includes two radially inwardly-extending flanges 121. Eachflange 121 includes a flange face 123 facing axially inwardly toward theraceway 122.

The inner ring 130 includes at least one radially outwardly-extendingflange 131 at one axial end of the raceway 132 defined on the inner ring130. The flange 131 includes a flange face 133 facing axially inwardlytoward the raceway 132.

Each roller 140 has two end faces 141 a and 141 b, and an outer diametersurface 146 that engages and rolls on the raceways 122, 132. The endfaces 141 a, 141 b may be made substantially symmetrical to a centerradial plane (a plane perpendicular to roller axis) of the roller 140,however this need not be the case.

With reference to FIGS. 8 and 9, each end face 141 a, 141 b contains acurved profile 145 defined in an axial plane that passes through therotational axis 147 (See FIG. 9) of the roller 140. The curved profile145 is formed by multiple segments 151, 152, 153, and 154 as for exampleshown in FIGS. 8 and 9. It is to be understood that in FIG. 9, only thelower left corner of the roller 140 is illustrated with the profile 145for simplicity and clarity, but that at least the upper left corner ofthe end face 141 a would have the same profile 145 mirrored about theaxis 147. Each profile segment 151, 152, 153, and 154 is defined by amathematically described or defined curvature. Each segment 151, 152,153, and 154 can be a straight line, a portion of a circle, or a complexcurve described for example by logarithmic or exponential equations.

The profile segment 151 is a portion of a straight line whose curvatureradius is infinity. Profile segments 152 and 154 are portions of circleswith curvature radii of R_(B2) and R_(D2), respectively. The centers ofthese curvatures are at O_(B2) and O_(D2) respectively. Profile segments151 and 152 are blended at tangent point A. Profile segments 152 and 153are blended at a tangent point B. Profile segments 153 and 154 areblended at a tangent point D. Profile segment 153 extends from point Bto point D and includes point C. As such, profile segment 153 can bebroken into segment portions 153B and 153D. Profile segment 154 isblended with the body 146 or outer diameter of the roller 140 or a greencorner of the roller at point E. Unlike blending points (A-D), point Emay or may not be a tangent point.

Profile segment 153 is a logarithmic curve or logarithmic curvesdescribed by the following equations in local x-y coordinate systemwhose origin is at the central contact point indicated by the referencepoint C or 161, with the x-axis being tangent to the roller end profileat the contact point C. The angle b represents the contact angle, whichis also the rotation angle between the local x-y and global X_(G)-Y_(G)coordinate systems.

$\begin{matrix}\begin{matrix}{y = {{- A_{b}}\log_{e}\left\{ {1 - {\left( {1 - e^{- \frac{y_{b}}{A_{b}}}} \right)\left( \frac{x}{l_{b}} \right)^{2}}} \right\}}} & {x \leq 0}\end{matrix} & \left( {1a} \right) \\\begin{matrix}{y = {{- A_{d}}\log_{e}\left\{ {1 - {\left( {1 - e^{- \frac{y_{d}}{A_{d}}}} \right)\left( \frac{x}{l_{d}} \right)^{2}}} \right\}}} & {x \geq 0}\end{matrix} & \left( {1b} \right)\end{matrix}$

where A_(b) and A_(d) are constants related to deflection of the contactsurfaces in y-direction under nominal design load (e.g., in someembodiments may vary from 1-100 microns, or more preferably from 10-25microns); l_(b), l_(d), y_(b) and y_(d) are the distances as defined inFIG. 10. More specifically, l_(b) is a distance in the local x-directionbetween point C and point B, l_(d) is a distance in the localx-direction between point C and point D, y_(b) is a distance in thelocal y-direction between point C and point B, and y_(d) is a distancein the local y-direction between point C and point D.

The logarithmic curves of segment portion 153B (CB) and 153D (CD) aredescribed by equations (1a) and (1b), respectively, and havecontinuously variable curvature radii. For example, at the startingpoint C, the curvature radii for CB and CD are, respectively,

$\begin{matrix}{R_{C -} = \frac{l_{b}^{2}}{2\; {A_{b}\left( {1 - e^{- \frac{y_{b}}{A_{b}}}} \right)}}} & \left( {2a} \right) \\{R_{C +} = \frac{l_{d}^{2}}{2{A_{d}\left( {1 - e^{- \frac{y_{d}}{A_{d}}}} \right)}}} & \left( {2b} \right)\end{matrix}$

At the end ending points (B or D) of the logarithmic curves (CB and CD),the curvature radii are, respectively,

$\begin{matrix}{R_{B} = {\frac{l_{b}}{2} \cdot \frac{\left\lbrack {{4\left( \frac{A_{b}}{l_{b}} \right)^{2}\left( {e^{\frac{y_{b}}{A_{b}}} - 1} \right)^{2}} + 1} \right\rbrack^{3/2}}{\left( \frac{A_{b}}{l_{b}} \right)\left( {e^{\frac{y_{b}}{A_{b}}} - 1} \right)\left( {{2e^{\frac{\gamma_{b}}{A_{b}}}} - 1} \right)}}} & \left( {3a} \right) \\{R_{D} = {\frac{l_{d}}{2} \cdot \frac{\left\lbrack {{4\left( \frac{A_{d}}{l_{d}} \right)^{2}\left( {e^{\frac{y_{d}}{A_{d}}} - 1} \right)^{2}} + 1} \right\rbrack^{3/2}}{\left( \frac{A_{d}}{l_{d}} \right)\left( {e^{\frac{y_{d}}{A_{d}}} - 1} \right)\left( {{2e^{\frac{y_{d}}{A_{d}}}} - 1} \right)}}} & \left( {3b} \right)\end{matrix}$

In general, the following inequalities hold true,

R _(C−) ≥R _(B)  (4a)

R _(C+) ≥R _(D)  (4b)

At the center of the contact point C, the curvature radii of thelogarithmic curves are the largest. Therefore, the curvature radius at agiven point decreases as the point moves along the curve away from thecenter of the contact point C.

It may be desirable to select design parameters such that the followingequations hold true,

R _(C−) =R _(C+)  (5a)

R _(B2) =R _(B)  (5b)

R _(D2) =R _(D)  (5c)

where R_(B2) and R_(D2) are curvature radii of circular segments AB andDE, respectively.

FIG. 11 shows a graphical example of a multi-segment roller end profileaccording to the current invention. In this example, the relationshipsset forth in equations (5a)-(5c) were incorporated.

With reference to FIG. 12, the locations of the profile segments 151,152, 153, and 154 of the rollers 140 are designed such that when theroller 140 is assembled and set in operation in a bearing 100 underthrust load, the contact between roller end 141 a or 141 b and themating flange face 123 and/or 133 starts at point 161. A footprint 162is developed as contact load increases. The size and shape of thefootprint 162 change as contact load increases. At a predetermineddesign load for the bearing 100, the contract footprint isnon-elliptical.

Profile segments 152 and 154 adjacent to the principal profile segment153 need not be portions of circles. They can be, for example, beportions of exponential curves or portions of logarithmic curves. In yetother alternatives, the profile segments 152, 154 might be extensions ofthe logarithmic curves used for the principle profile segment 153. Inyet other embodiments, there need not be additional, adjacent profilesegments 152 and 154. Instead, the principle segment 153 can be the solesegment of the curved profile 145.

The above-mentioned multi-segment roller end profiles can also, oralternatively, be made on flange faces 123 and/or 133. FIG. 13illustrates the flange face 133, but can also represent the flange faces123.

FIG. 13 depicts a roller bearing with rollers 140′ having conical rollerends 141′. The profile of the mating face 133′ of the flange 131′ ismathematically described by multi-segment curves. The profile has atleast three segments 134, 135 and 136. Any two adjacent segments aretangent to each other. When the roller 140′ is brought into contact withthe mating flange 131′ at the contact point 161, a non-ellipticalcontact footprint develops at a predetermined design load. Thenon-elliptical contact footprint corresponds to the logarithmic curvesof the profile segment 135, which can have same curvature as the profilesegment 153 described above. The aspect ratio of the contact footprintincreases as the contact load further increases.

Once again, a non-elliptical contact footprint can be obtained bycomposite profiles at the contact location between the roller end andthe mating flange face. This is to say that multi-segment profiles canbe placed either on the roller end, on the flange face, or on both theroller end and the flange faces. The profile segment or segments at thecenter of the contact footprint is a portion of a logarithmic curve thathas continuously changing curvature radii. The curvature radii of thelogarithmic segment are no less than that of the segments adjacent tothe logarithmic segment.

Various features and advantages of the invention are set forth in thefollowing claims.

1. A roller bearing comprising: an inner race ring; an outer race ring;and a roller arranged between and in contact with the inner and outerrings; wherein the bearing has a flange on the inner race ring at oneaxial end, and a flange on the outer race ring at an opposite axial end;wherein the roller has a profiled roller end including at least oneprincipal segment intermediate two additional segments, the principlesegment being tangentially blended with the two additional segments;wherein the principle segment has a first curvature that is differentfrom the respective curvatures of the two additional segments; andwherein the curvatures of each of the principle segment and the twoadditional segments are portions of a circle, and wherein the firstcurvature has a greater radius of curvature than the respective radii ofcurvatures of the two additional segments.
 2. (canceled)
 3. (canceled)4. The roller bearing of claim 1, wherein the respective radii ofcurvatures of the two additional segments are different.
 5. (canceled)6. The roller bearing of claim 1, further comprising a fourth segmenttangentially blended with one of the two additional segments.
 7. Theroller bearing of claim 1, wherein the profiled roller end is at a firstaxial end of the roller, and wherein the roller includes a secondprofiled roller end at a second axial end of the roller, wherein thesecond profiled roller end includes at least one principal segmentintermediate two additional segments, the principle segment beingtangentially blended with the two additional segments, and wherein theprinciple segment has a first curvature that is different from therespective curvatures of the two additional segments.
 8. The rollerbearing of claim 1, wherein a contact footprint defined between theprofiled roller end and a mating flange on the inner ring or the outerring is non-elliptical in shape when the bearing operates at apredetermined design load.
 9. A roller bearing comprising: an inner racering; an outer race ring; and a roller arranged between and in contactwith the inner and outer rings; wherein the bearing has a flange on theinner race ring at one axial end, and a flange on the outer race ring atan opposite axial end; wherein at least one of the flanges is profiledto include at least one principal segment intermediate two additionalsegments, the principle segment being tangentially blended with the twoadditional segments; wherein the principle segment has a first curvaturethat is different from the respective curvatures of the two additionalsegments; and wherein the curvatures of each of the principle segmentand the two additional segments are portions of a circle, and whereinthe first curvature has a greater radius of curvature than therespective radii of curvatures of the two additional segments. 10.(canceled)
 11. (canceled)
 12. The roller bearing of claim 9, wherein therespective radii of curvatures of the two additional segments aredifferent.
 13. (canceled)
 14. The roller bearing of claim 9, wherein theroller includes a roller end that engages the profiled flange, theroller end being spherical.
 15. The roller bearing of claim 9, whereinthe roller includes a roller end that engages the profiled flange, theroller end being conical.
 16. The roller bearing of claim 9, wherein acontact footprint defined between the profiled flange and an end of theroller is non-elliptical in shape when the bearing operates at apredetermined design load. 17-26. (canceled)
 27. The roller bearing ofclaim 1, wherein the roller has a roller axis and a radius R, andwherein the principle segment has a center of curvature offset from theroller axis by a distance less than 0.5 R.
 28. The roller bearing ofclaim 27, wherein centers of curvature of the two additional segmentsare offset from the roller axis by a distance greater than 0.5 R.